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Software Package for Modeling III-Nitride QW Laser Diodes
and Light Emitting Devices
Mikhail V. Kisin*, Robert G. W. Brown and Hussein S. El-Ghoroury
Ostendo Technologies, Inc. *Corresponding author: 6185 Paseo del Norte, Ste.200, Carlsbad, CA 92011, [email protected]
Abstract: We present a modeling software
package developed at Ostendo Technologies for
analysis and design of semiconductor laser and
light-emitting diodes. The current database of
material parameters supports complete group of
III-Nitride alloys used in visible spectrum
applications and can be readily extended to all
III-V compounds.
Keywords: Optoelectronics, laser diodes, light-
emitting diodes, nitrides, III-V compounds.
1. Introduction
Nitride-based photonic devices lead the way
in developing visible and UV optical range
applications with electrically pumped laser
diodes (LD) and light-emitting devices (LED)
being in the highest demand.
Modeling of optoelectronic devices is an
extremely complicated task. It involves a
combination of strongly interrelated physical
phenomena taking place at different space and
time scales – from angstroms and picoseconds in
optically active quantum wells (QW) to dc
transition times and carrier diffusion lengths
limited by injection and external modulation.
At least four basic software blocks or
modules should be involved in full-scale
LD/LED modeling and design addressing,
correspondingly, the physics in microscopic
Figure 1. Flowchart of device modeling stages.
active regions, the transport in the diode
structure, the optical waveguiding, and the
thermal management. The database of material
parameters is yet another important building
block of the software as illustrated in Figure 1.
In this work, we present full-scale modeling
software package developed at Ostendo
Technologies for analysis and design of III-V
semiconductor active optoelectronic
components. The current database of material
parameters supports complete group of III-
Nitride alloys used in visible spectrum
applications and can be readily extended to all
III-V compounds with corresponding extension
of the spectral range of the devices [1].
2. Use of COMSOL Multiphysics
All the software components are COMSOL-
based with physical models and databases
originally developed at Ostendo Technologies.
No specific COMSOL modules have been
employed in our programs. Special effort has
gone into developing the Micro module [1,2].
Self-consistent multi-band quantum-mechanical
model for carrier energy spectrum in active QWs
has been implemented and solved with
COMSOL eigenvalue solver. Drift-diffusion
equations of our Transport module are solved by
nonlinear stationary solver. At this stage of
development, all modeling is one-dimensional.
Figure 2. Band profiles and eigenstates in active QWs
Excerpt from the Proceedings of the COMSOL Conference 2009 Boston
Figure 3. Injected current distribution (left) and injection, radiative, and waveguide/cladding leakage coefficients
versus injection level (right) at different temperatures: solid – 300K, dash – 400K, dash-dot – 500K.
Figure 4. Band profiles and radiative/nonradiative recombination rate distribution at threshold level in three-QW
structure (left); Fc/ Fh - quasi-Fermi levels. Relative QW population dynamics (right); color identifies the QW.
Figure 5. Left: TE gain (blue) and spontaneous emission spectra (black). Right: material gain and emission wavelength
as a function of QW radiative current level; dashed lines illustrate effect of inhomogeneous broadening.
Figure 6. Temperature dependence of QW gain (blue)
and emission wavelength for main transition (black),
spontaneous emission (green) and peak gain (red).
Dashed lines illustrate the effect of inhomogeneous
broadening on peak gain and wavelength.
3. Results
The Micro module provides detailed
information about microscopic structure of
lasing states, allows calculation of electron and
hole energy spectra and modeling of QW optical
characteristics. Module output includes: (1) self-
consistent band profiles including strain effect,
spontaneous- and piezo-polarization; (2) QW
subband dispersions with band-mixing and
nonparabolicity; (3) confined energy levels and
subband DOS; (4) optical matrix elements and
optical anisotropy coefficients; (5) emission
wavelength shift with injection; (6) carrier
statistical distribution and subband populations;
(7) spontaneous and stimulated emission rates;
(8) optical gain spectra, peak optical gain, and
induced refractive index change; (9) differential
optical gain (with respect to concentration and
radiative current); (10) transparency
concentration level and corresponding radiative
current.
The Transport module provides distribution
of injected carriers and corresponding
recombination rates throughout the structure as a
function of injection current. Module output
includes: (1) self-consistent band profiles and
charge carrier distributions in active region; (2)
injected current distribution; (3) radiative and
nonradiative recombination rate distributions; (4)
relative QW populations; (5) free-carrier
absorption distribution; (6) I-V characteristics;
(7) injection and radiative efficiency; (8) leakage
current.
The Optical module provides transverse
optical mode distribution and estimation of
modal refractive index. Module output includes:
(1) refractive index profile at lasing wavelength
and modal refractive index; (2) transverse optical
mode distribution; (3) QW optical confinement
factors.
At this level of program development the
heat management has not been yet independently
addressed. In all modules, temperature effects
are treated parametrically. Self-heating effect
estimation is based on the experimentally
determined structure thermo-impedance
The Final design module combines the
results obtained in the Micro, Transport, and
Optical modules. The final design module is
based on phenomenological characteristics
approximating the more detailed results of each
particular module, like efficiency parameters,
gain coefficients, confinement and loss factors,
etc.
Module output includes: (1) L-I
characteristics; (2) threshold current and
characteristic temperature; (3) differential
quantum (slope) efficiency and characteristic
temperature; (4) output optical power and wall-
plug efficiency; (5) dependence of threshold and
efficiency on the emission wavelength;
(6) dependence of LD threshold and efficiency
on the total number of QWs.
Input/Output interface programs generate
modeling log file automatically assembling
tables of calculated parameters and figures of
modeled device characteristics.
Figure 7. Refractive index and main optical mode
profile for 3-QW LD structure on sapphire substrate.
Figure 8. L-I-V characteristics of 3-QW LD structure
at different temperatures.
Figure 9. Temperature dependence of differential
quantum efficiency and threshold current density.
Figure 10. Active region temperature rise for DC laser
operation. Red crosses mark the threshold values.
4. Exemplary calculation
We illustrate the software capability by
modeling a typical blue-range laser diode with
symmetrical optical waveguide layout
comprising active region with three 3 nm wide
GaInN QWs. Figures 2-10 exemplify the design
process and illustrate the main characteristics of
the structure.
5. Conclusions
Development of physics-based modeling
tools with open access to the model contents
utilizing COMSOL Multiphysics is the most
efficient way to design elaborate contemporary
optoelectronic devices based on novel physical
principles and/or new material systems.
COMSOL Multiphysics make possible creating
flexible and yet comprehensive physical models
which facilitate the design even for the most
untraditional devices. We provide a brief
description of full-scale modeling tools
developed at Ostendo Technologies, Inc. for
design of III-Nitride based active optoelectronic
devices. Already, using this COMSOL-based
software package we have made useful
observations on the design and performance of
GaInN laser diodes [3, 4].
6. References 1. M. V. Kisin, "Modeling of the Quantum Well and
Cascade Semiconductor Lasers using 8-Band
Schrödinger and Poisson Equation System," in
COMSOL Conference 2007, Newton, MA, USA,
(2007)
2. M. V. Kisin, R. G. W. Brown, and H. S. El-
Ghoroury, "Modeling of III-Nitride Quantum Wells
with Arbitrary Crystallographic Orientation for
Nitride-Based Photonics," in COMSOL Conference
2008, Boston, MA, USA, (2008).
3. M. V. Kisin, R. G. W. Brown, and H. S. El-
Ghoroury, "Optimum quantum well width for III-
nitride nonpolar and semipolar laser diodes," Appl.
Phys. Lett., 94, 021108-3 (2009).
4. M. V. Kisin, R. G. W. Brown, and H. S. El-
Ghoroury, "Optical characteristics of III-nitride
quantum wells with different crystallographic
orientations," J. Appl. Phys., 105, 013112-5, (2009).